Friday, 22 April 2016

At the heart of game theory is the notion that we can strip away details of a particular setting to focus on the key strategic incentives that matter. Hence, two very different looking settings can give rise to the same game. For example, contributing to charity may be strategically equivalent to not dropping litter. This stripping away of detail makes game theory a 'general theory' rather than a list of case studies. But, the constant danger is to strip away details that matter.

Framing effects are one illustration of this danger. Daniel Kahneman and Amos Tversky very powerfully illustrated that people can make different decisions depending on how a decision is framed. (See, for example, their 1981 article in Science on 'the framing of decisions and psychology of choice'.) Strategically irrelevant aspects of a setting may, therefore, matter. Recent years have seen a burgeoning number of studies looking at framing effects in public good games. The basic question of interest is whether people more willing to cooperate in some frames than others? For instance, is someone more likely to give to charity than not drop litter?

It has become routine to say that the evidence of framing effects in public good games is mixed. And this, in a sense, is undeniable because there are some studies that show large framing effects and others that show none. But why are we getting these mixed results? There are lots of dimensions along which a public good game can differ, of which here are three:

In a pioneering study, James Andreoni focussed on an externality dimension. In a positive frame the positive externality of contributing is emphasized - if you contribute others gain - while in a negative frame the negative externality of not contributing is emphasized - if you do not contribute others lose.

Much attention has also focussed on a choice dimension. In a give frame the choice people have to make is how much to contribute while in a take frame the choice people have to make is how much to not contribute.

There is an initial allocation dimension. A person can initially start with money (private good) or public good.

Just putting these three dimensions together gives at least 2x2x2 = 8 different frames. For instance, we can have a positive-give-some frame where a person starts with money, can give-some to charity and the charity emphasizes the positive externality of doing so. Or, we can have a positive-keep-some frame where a person starts with money, can keep-some from not going to the taxman and the taxman emphasizes the positive externality of paying taxes. Or, we can have a negative-leave-some frame where a person starts with a clean river, they can leave-some cleanliness (by not polluting) and environment groups emphasize the negative externality from pollution.

To understand why framing results are mixed it seems clear that we should carefully distinguish between different framing dimensions. In all likelihood some framing dimensions matter and others don't. In a recent paper, published in the Journal of the Economic Science Association, I argue that currently not enough account is being taken of different framing dimensions; framing effects are being lumped together in a way that means we miss key insight. In particular, it has implicitly been assumed by many that the externality and choice dimensions are the same - positive going with give and negative with take. But these dimensions need to be kept separate - positive can go with take and negative with give.
Once we split apart dimensions the evidence seems to suggest that the externality dimension does matter while the choice dimension does not (in terms of average cooperation). This means that the mixed results in the literature become more easily understood, because some studies focus on the externality dimension (and find a strong effect) while others focus on the choice dimension (and find little effect).
In time, it would not surprise me if the 'externality dimension matters while choice dimension does not' result needs revision. For instance, only 3 of the 8 possible frames alluded to above have been widely studied. The more general argument, that we need to carefully distinguish between framing dimensions, must, however, be taken seriously if we are to find out what causes framing effects. And it is surprising how little we do know about what causes them. While the number of framing experiments grows by the month there is very little by way of theoretical work to make sense of the results. (A study by Martin Dufwenberg, Simon Gachter and Heike Hennig-Schmidt on 'the framing of games and the psychology of play' is one notable exception.) A deeper theoretical understanding should surely be a priority for future work.